Question 1

Write four additional terms of the geometric sequence.
-Find the first five terms of the sequence with first term 8 and nth term $$a _ { n } = 2 a _ { n - 1 }$$

Accepted Answer

A)  16, 32, 64, 128, 256 
B)  8, 16, 32, 64, 128 
C)  8, 40, 45, 50, 55 
D)  0, 5, 40, 45, 50 
A)  16, 32, 64, 128, 256 
B)  8, 16, 32, 64, 128 
C)  8, 40, 45, 50, 55 
D)  0, 5, 40, 45, 50

Question 2

Graph.
-$( x - 1 ) y = 1$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 3

Write the binomial expansion of the expression.
-$$\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }$$

Accepted Answer

A)  $64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$ 
B)  $\left( 16 x ^ { 4 } - 8 x ^ { 2 } + 1 \right) ^ { 3 }$ 
C)  $256 x ^ { 8 } + 64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$ 
D)  $64 x ^ { 3 } - 48 x ^ { 2 } + 12 x - 1$ 
A)  $64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$ 
B)  $\left( 16 x ^ { 4 } - 8 x ^ { 2 } + 1 \right) ^ { 3 }$ 
C)  $256 x ^ { 8 } + 64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$ 
D)  $64 x ^ { 3 } - 48 x ^ { 2 } + 12 x - 1$

Question 4

Write the binomial expansion of the expression.
-$$( 2 x - 1 ) ^ { 5 }$$

Accepted Answer

A)  $32 x ^ { 5 } - 80 x ^ { 4 } + 80 x ^ { 3 } - 40 x ^ { 2 } + 10 x - 1$ 
B)  $32 x ^ { 5 } - 16 x ^ { 4 } + 8 x ^ { 3 } - 4 x ^ { 2 } + 2 x - 1$ 
C)  $32 x ^ { 5 } + 10 x ^ { 4 } - 40 x ^ { 3 } - 40 x ^ { 2 } + 10 x - 1$ 
D)  $\left( 4 x ^ { 2 } - 4 x + 1 \right) ^ { 5 }$ 
A)  $32 x ^ { 5 } - 80 x ^ { 4 } + 80 x ^ { 3 } - 40 x ^ { 2 } + 10 x - 1$ 
B)  $32 x ^ { 5 } - 16 x ^ { 4 } + 8 x ^ { 3 } - 4 x ^ { 2 } + 2 x - 1$ 
C)  $32 x ^ { 5 } + 10 x ^ { 4 } - 40 x ^ { 3 } - 40 x ^ { 2 } + 10 x - 1$ 
D)  $\left( 4 x ^ { 2 } - 4 x + 1 \right) ^ { 5 }$

Question 5

Write the equation for the shape described.
-The circle with center at $( - 6 , - 2 )$, passing through $( - 3,2 )$

Accepted Answer

A)  $( x - 6 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$ 
B)  $( x + 2 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 9$ 
C)  $( x - 2 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 9$ 
D)  $( x + 6 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$ 
A)  $( x - 6 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$ 
B)  $( x + 2 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 9$ 
C)  $( x - 2 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 9$ 
D)  $( x + 6 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$

Question 6

Graph the region determined by the inequality in the context of the application.
-In order to make a profit an automobile dealer must sell at least 200 vehicles a month. The dealer plans to sell x units of one model and y units of another model. This situation can be modeled by the inequality $$x + y \geq 200$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 7

A new firm loses $3600 in its first month, but its profit increases by $700 in each succeeding month. What is its profit in the 8th month?

Accepted Answer

A)  $9200 
B)  $1300 
C)  $2000 
D)  $8500 
A)  $9200 
B)  $1300 
C)  $2000 
D)  $8500

Question 8

Find the sum of the series, if possible.
-$$\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 3 } \right) ^ { i }$$

Accepted Answer

A)  2 
B)  $\frac { 3 } { 2 }$ 
C)  Not possible, infinite 
D)  1 
A)  2 
B)  $\frac { 3 } { 2 }$ 
C)  Not possible, infinite 
D)  1

Question 9

Evaluate the derivative.
-$f ^ { \prime } ( 3 )$ if $f ^ { \prime } ( x ) = \frac { \left( x ^ { 2 } - 5 \right) ( 4 ) - ( 2 x ) ( 4 x ) } { \left( x ^ { 2 } - 5 \right) ^ { 2 } }$

Accepted Answer

A)  $\frac { 4 } { 9 }$ 
B)  $- 1$ 
C)  $- 2$ 
D)  $- \frac { 7 } { 2 }$ 
A)  $\frac { 4 } { 9 }$ 
B)  $- 1$ 
C)  $- 2$ 
D)  $- \frac { 7 } { 2 }$

Question 10

Draw the graph of the equation.
-$x=3 \sqrt{1-y^{2}}$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Draw the graph of the equation.
-$$
y=\sqrt{x+2}
$$

Accepted Answer

A)   
B)   
C)   
D)   
A)   
B)   
C)   
D)

Question 12

A man borrowed $3000 at 10% interest compounded annually. If he paid off the loan in full at the end of 4 years, how much did he pay? Round your answer to the nearest cent.

Accepted Answer

A)  $4200.00 
B)  $4392.30 
C)  $3300.00 
D)  $1392.30 
A)  $4200.00 
B)  $4392.30 
C)  $3300.00 
D)  $1392.30

Question 13

Draw the graph of the equation.
-$3 x^{2}+4 y^{2}-18 x+40 y+115=0$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Evaluate the expression.
-$\frac { 12 ! } { 6 ! 6 ! }$

Accepted Answer

A)  462 
B)  1848 
C)  924 
D)  665,280 
A)  462 
B)  1848 
C)  924 
D)  665,280

Question 15

Write four additional terms of the geometric sequence.
-Find the first four terms of the sequence with first term 9 and nth term $$a _ { n } = a _ { n - 1 } + 4$$

Accepted Answer

A)  13, 17, 21, 25 
B)  0, 4, 8, 12 
C)  9, 4, 8, 12 
D)  9, 13, 17, 21 
A)  13, 17, 21, 25 
B)  0, 4, 8, 12 
C)  9, 4, 8, 12 
D)  9, 13, 17, 21

Question 16

A pendulum bob swings 6.0 cm on its first oscillation. On each subsequent oscillation the bob travels $\frac { 1 } { 3 }$ of the previous distance. Find the total distance the bob travels before coming to rest.

Accepted Answer

A)  9.0 cm 
B)  12.0 cm 
C)  13.0 cm 
D)  13.3 cm 
A)  9.0 cm 
B)  12.0 cm 
C)  13.0 cm 
D)  13.3 cm

Question 17

Calculus can be used to find the slope of the line tangent to a curve. The slope of the tangent to the curve $y = f ( x ) \text { at } x = a$ is f'(a). Use f'(x) to find the slope of the tangent to $y = f ( x )$ at the given value of x.
-$f ^ { \prime } ( x ) = 6 x ^ { 3 } - 2 x ^ { 2 } + 5 x - 19$ at $x = - 2$

Accepted Answer

A)  $- 69$ 
B)  85 
C)  $- 75$ 
D)  $- 85$ 
A)  $- 69$ 
B)  85 
C)  $- 75$ 
D)  $- 85$

Question 18

Write the equation of the circle with the given center and radius.
-center $( - 10,1 )$, radius $\sqrt { 13 }$

Accepted Answer

A)  $( x + 1 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 169$ 
B)  $( x - 10 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 13$ 
C)  $( x + 10 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 13$ 
D)  $( x - 1 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 169$ 
A)  $( x + 1 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 169$ 
B)  $( x - 10 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 13$ 
C)  $( x + 10 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 13$ 
D)  $( x - 1 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 169$

Question 19

Write four additional terms of the geometric sequence.
-6, 18, 54, . . .

Accepted Answer

A)  162, 486, 1458, 4374 
B)  216, 864, 3456, 13,824 
C)  162, 486, 1468, 4399 
D)  108, 216, 432, 864 
A)  162, 486, 1458, 4374 
B)  216, 864, 3456, 13,824 
C)  162, 486, 1468, 4399 
D)  108, 216, 432, 864

Question 20

Write four additional terms of the geometric sequence.
-A man earned $3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15th year?

Accepted Answer

A)  $5600 
B)  $9000 
C)  None of these 
D)  $8600 
A)  $5600 
B)  $9000 
C)  None of these 
D)  $8600

Write four additional terms of the geometric sequence. -Find the first five terms of the sequence with first term 8 and nth term $a _ { n } = 2 a _ { n - 1 }$

Graph. - $( x - 1 ) y = 1$

Write the binomial expansion of the expression. - $\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }$

Write the binomial expansion of the expression. - $( 2 x - 1 ) ^ { 5 }$

Write the equation for the shape described. -The circle with center at $( - 6 , - 2 )$ , passing through $( - 3,2 )$

A new firm loses $3600 in its first month, but its profit increases by $700 in each succeeding month. What is its profit in the 8th month?

Find the sum of the series, if possible. - $\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 3 } \right) ^ { i }$

Evaluate the derivative. - $f ^ { \prime } ( 3 )$ if $f ^ { \prime } ( x ) = \frac { \left( x ^ { 2 } - 5 \right) ( 4 ) - ( 2 x ) ( 4 x ) } { \left( x ^ { 2 } - 5 \right) ^ { 2 } }$

Draw the graph of the equation. - $x=3 \sqrt{1-y^{2}}$ $Draw the graph of the equation. - x=3 \sqrt{1-y^{2}}$

Draw the graph of the equation. - $y=\sqrt{x+2}$ $Draw the graph of the equation. - y=\sqrt{x+2}$

A man borrowed $3000 at 10% interest compounded annually. If he paid off the loan in full at the end of 4 years, how much did he pay? Round your answer to the nearest cent.

Draw the graph of the equation. - $3 x^{2}+4 y^{2}-18 x+40 y+115=0$ $Draw the graph of the equation. - 3 x^{2}+4 y^{2}-18 x+40 y+115=0$

Evaluate the expression. - $\frac { 12 ! } { 6 ! 6 ! }$

Write four additional terms of the geometric sequence. -Find the first four terms of the sequence with first term 9 and nth term $a _ { n } = a _ { n - 1 } + 4$

A pendulum bob swings 6.0 cm on its first oscillation. On each subsequent oscillation the bob travels $\frac { 1 } { 3 }$ of the previous distance. Find the total distance the bob travels before coming to rest.

Write the equation of the circle with the given center and radius. -center $( - 10,1 )$ , radius $\sqrt { 13 }$

Write four additional terms of the geometric sequence. -6, 18, 54, . . .

Write four additional terms of the geometric sequence. -A man earned $3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15th year?

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Filters

Exam 8: Special Topics in Algebra

Write four additional terms of the geometric sequence. -Find the first five terms of the sequence with first term 8 and nth term an=2an−1a _ { n } = 2 a _ { n - 1 }an​=2an−1​

Graph. - (x−1)y=1( x - 1 ) y = 1(x−1)y=1

Write the binomial expansion of the expression. - (4x2−1)3\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }(4x2−1)3

Write the binomial expansion of the expression. - (2x−1)5( 2 x - 1 ) ^ { 5 }(2x−1)5

Write the equation for the shape described. -The circle with center at (−6,−2)( - 6 , - 2 )(−6,−2) , passing through (−3,2)( - 3,2 )(−3,2)

A new firm loses $3600 in its first month, but its profit increases by $700 in each succeeding month. What is its profit in the 8th month?

Find the sum of the series, if possible. - ∑i=1∞2(13)i\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 3 } \right) ^ { i }∑i=1∞​2(31​)i

Evaluate the derivative. - f′(3)f ^ { \prime } ( 3 )f′(3) if f′(x)=(x2−5)(4)−(2x)(4x)(x2−5)2f ^ { \prime } ( x ) = \frac { \left( x ^ { 2 } - 5 \right) ( 4 ) - ( 2 x ) ( 4 x ) } { \left( x ^ { 2 } - 5 \right) ^ { 2 } }f′(x)=(x2−5)2(x2−5)(4)−(2x)(4x)​

Draw the graph of the equation. - x=31−y2x=3 \sqrt{1-y^{2}}x=31−y2​

Draw the graph of the equation. - y=x+2y=\sqrt{x+2}y=x+2​

A man borrowed $3000 at 10% interest compounded annually. If he paid off the loan in full at the end of 4 years, how much did he pay? Round your answer to the nearest cent.

Draw the graph of the equation. - 3x2+4y2−18x+40y+115=03 x^{2}+4 y^{2}-18 x+40 y+115=03x2+4y2−18x+40y+115=0

Evaluate the expression. - 12!6!6!\frac { 12 ! } { 6 ! 6 ! }6!6!12!​

Write four additional terms of the geometric sequence. -Find the first four terms of the sequence with first term 9 and nth term an=an−1+4a _ { n } = a _ { n - 1 } + 4an​=an−1​+4

A pendulum bob swings 6.0 cm on its first oscillation. On each subsequent oscillation the bob travels 13\frac { 1 } { 3 }31​ of the previous distance. Find the total distance the bob travels before coming to rest.

Write the equation of the circle with the given center and radius. -center (−10,1)( - 10,1 )(−10,1) , radius 13\sqrt { 13 }13​

Write four additional terms of the geometric sequence. -6, 18, 54, . . .

Write four additional terms of the geometric sequence. -A man earned $3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15th year?

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Filters

Write four additional terms of the geometric sequence. -Find the first five terms of the sequence with first term 8 and nth term $a _ { n } = 2 a _ { n - 1 }$

Graph. - $( x - 1 ) y = 1$

Write the binomial expansion of the expression. - $\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }$

Write the binomial expansion of the expression. - $( 2 x - 1 ) ^ { 5 }$

Write the equation for the shape described. -The circle with center at $( - 6 , - 2 )$ , passing through $( - 3,2 )$

Find the sum of the series, if possible. - $\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 3 } \right) ^ { i }$

Evaluate the derivative. - $f ^ { \prime } ( 3 )$ if $f ^ { \prime } ( x ) = \frac { \left( x ^ { 2 } - 5 \right) ( 4 ) - ( 2 x ) ( 4 x ) } { \left( x ^ { 2 } - 5 \right) ^ { 2 } }$

Draw the graph of the equation. - $x=3 \sqrt{1-y^{2}}$ $Draw the graph of the equation. - x=3 \sqrt{1-y^{2}}$

Draw the graph of the equation. - $y=\sqrt{x+2}$ $Draw the graph of the equation. - y=\sqrt{x+2}$

Draw the graph of the equation. - $3 x^{2}+4 y^{2}-18 x+40 y+115=0$ $Draw the graph of the equation. - 3 x^{2}+4 y^{2}-18 x+40 y+115=0$

Evaluate the expression. - $\frac { 12 ! } { 6 ! 6 ! }$

Write four additional terms of the geometric sequence. -Find the first four terms of the sequence with first term 9 and nth term $a _ { n } = a _ { n - 1 } + 4$

A pendulum bob swings 6.0 cm on its first oscillation. On each subsequent oscillation the bob travels $\frac { 1 } { 3 }$ of the previous distance. Find the total distance the bob travels before coming to rest.

Write the equation of the circle with the given center and radius. -center $( - 10,1 )$ , radius $\sqrt { 13 }$